참고문헌
- Bathe, K.J. and Wilson, E.L. (1976), Numerical Methods in Finite Element Analysis, Prentice-Hall, New Jersey.
- Cai, Z.Q., Gu, Y.X. and Zhong, W.X. (2001), "A new approach of computing Floquet transition matrix", Comput. Struct., 79(6), 631-635. https://doi.org/10.1016/S0045-7949(00)00169-3
- Chen, B.S., Gu, Y.X., Guan, Z.Q. and Zhang, H.W. (2001), "Nonlinear transient heat conduction analysis with precise time integration method", Numer. Heat Tr. B-Fund., 40(4), 325-341. https://doi.org/10.1080/104077901317091712
- Fu, M.H., Cheung, M.C. and Sheshenin, S.V. (2010), "Precise integration method for solving singular perturbation problems", Appl. Math. Mech., 31(11), 1463-1472. https://doi.org/10.1007/s10483-010-1376-x
- Fung, T.C. (1997), "A precise time-step integration method by step-response and impulsive-response matrices for dynamic problems", Int. J. Numer. Meth. Eng., 40(24), 4501-4527. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24<4501::AID-NME266>3.0.CO;2-U
- Fung, T.C. and Chen, Z.L. (2006), "Krylov precise time-step integration method", Int. J. Numer. Meth. Eng., 68(11), 1115-1136. https://doi.org/10.1002/nme.1737
- Gu, Y.X., Chen, B.S., Zhang, H.W. and Guan, Z.Q. (2001), "Precise time-integration method with dimensional expanding for structural dynamic equations", AIAA J., 39(12), 2394-2399. https://doi.org/10.2514/2.1248
- Hairer, E., Lubich, C. and Wanner, G. (2006), Geometric Numerical Integration: Structure-preserving Algorithm for Ordinary Differential Equations, 2nd Edition, Springer, New York.
- Hairer, E., Norsett, S.P. and Wanner, G. (1993), Solving Ordinary Differential Equations I-nonstiff Problems, 2nd Edition, Springer, Berlin.
- Hairer, E. and Wanner, G. (1996), Solving Ordinary Differential Equations II-stiff and Differential- Algebraic Problems, 2nd Edition, Springer, Berlin.
- Jia, L., Shi, W. and Guo, J. (2008), "Arbitrary-difference precise-integration method for the computation of electromagnetic transients in single-phase nonuniform transmission line", IEEE Trans. Power Del., 23(3), 1488-1494.
- Leung, A.Y.T. (2001), "Fast matrix exponent for deterministic or random excitations", Int. J. Numer. Meth. Eng., 50(2), 377-394. https://doi.org/10.1002/1097-0207(20010120)50:2<377::AID-NME29>3.0.CO;2-E
- Lin, J.H., Shen, W.P. and Williams, F.W. (1995), "A high precision direct integration scheme for structures subjected to transient dynamic loading", Comput. Struct., 56(1), 113-120. https://doi.org/10.1016/0045-7949(94)00537-D
- Lin, J.H., Shen, W.P. and Williams, F.W. (1997), "Accurate high-speed computation of non-stationary random structural response", Eng. Struct., 19(7), 586-593. https://doi.org/10.1016/S0141-0296(97)83154-9
- Lin, J.H., Shen, W.P. and Williams, F.W. (1997), "Accurate high-speed computation of non-stationary random structural response", Eng. Struct., 19(7), 586-593. https://doi.org/10.1016/S0141-0296(97)83154-9
- Moler, C. and Loan, C.V. (1978), "Nineteen dubious ways to compute the exponential of a matrix", SIAM Rev., 20(4), 801-836. https://doi.org/10.1137/1020098
- Moler, C. and Loan, C.V. (2003), "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later", SIAM Rev., 45(1), 1-46. https://doi.org/10.1137/SIREAD000045000001000001000001
- Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech.-ASCE, 85(3), 67-94.
- Shen, W.P., Lin, J.H. and Williams, F.W. (1995), "Parallel computing for the high precision direct integration method", Comput. Meth. Appl. M., 126(3-4), 315-331. https://doi.org/10.1016/0045-7825(95)00824-K
- Wang, M.F. and Au, F.T.K. (2007), "Precise integration method without inverse matrix calculation for structural dynamic equations", Earthq. Eng. Vib., 6(1), 57-64. https://doi.org/10.1007/s11803-007-0661-2
- Wang, M.F. and Au, F.T.K. (2006), "Assessment and improvement of precise time step integration method", Comput. Struct., 84(12), 779-786. https://doi.org/10.1016/j.compstruc.2006.02.001
- Wang, M.F. and Au F.T.K. (2009), "Precise integration methods based on Lagrange piecewise interpolation polynomials", Int. J. Numer. Meth. Eng., 77(7), 998-1014. https://doi.org/10.1002/nme.2444
- Wang, M.F. (2011), "Reduced-order precise integration methods for structural dynamic equations", Int. J. Numer. Meth. Biomed. Eng., 27(10), 1569-1582. https://doi.org/10.1002/cnm.1382
- Zhang, H.W., Chen, B.S. and Gu, Y.X. (2001), "An adaptive algorithm of precise integration for transient analysis", ACTA Mech. Solida Sin., 14(3), 215-224.
- Zhang, H.W., Zhang, X.W. and Chen, J.S. (2003), "A new algorithm for numerical solution of dynamic elastic- plastic hardening and softening problems", Comput. Struct., 81(17), 1739-1749. https://doi.org/10.1016/S0045-7949(03)00167-6
- Zhong, W.X. (2004), "On precise integration method", J. Comput. Appl. Math., 163(1), 59-78. https://doi.org/10.1016/j.cam.2003.08.053
- Zhong, W.X. and Williams, F.W. (1994), "A precise time step integration method", P. I. Mech. Eng. C-J. Mec., 208(6), 427-430. https://doi.org/10.1243/PIME_PROC_1994_208_148_02
- Zhong, W.X., Zhu, J. and Zhong, X.X. (1996), "On a new time integration method for solving time dependent partial differential equations", Comput. Meth. Appl. M., 130(1-2), 163-178. https://doi.org/10.1016/0045-7825(95)00876-4
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